সমাধান - জ্যামিতিক ধারা

সিরিজের সাধারণ রূপ খুঁজে পেতে, প্রথম পদ: $$a=111$$ এবং সাধারণ অনুপাত: $$r=0.018018018018018018$$ জ্যামিতিক সিরিজের সূত্রে প্লাগ করুন:

$$a_1=111$$

$$a_2=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{2-1}=111\cdot {0.018018018018018018}^1=111\cdot 0.018018018018018018=2$$

$$a_3=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{3-1}=111\cdot {0.018018018018018018}^2=111\cdot 0.00032464897329762194=0.036036036036036036$$

$$a_4=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{4-1}=111\cdot {0.018018018018018018}^3=111\cdot 5.849531050407603E-06=0.0006492979465952439$$

$$a_5=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{5-1}=111\cdot {0.018018018018018018}^4=111\cdot 1.0539695586320005E-07=1.1699062100815205E-05$$

$$a_6=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{6-1}=111\cdot {0.018018018018018018}^5=111\cdot 1.8990442497873883E-09=2.107939117264001E-07$$

$$a_7=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{7-1}=111\cdot {0.018018018018018018}^6=111\cdot 3.421701350968267E-11=3.798088499574777E-09$$

$$a_8=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{8-1}=111\cdot {0.018018018018018018}^7=111\cdot 6.165227659402283E-13=6.843402701936534E-11$$

$$a_9=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{9-1}=111\cdot {0.018018018018018018}^8=111\cdot 1.1108518305229338E-14=1.2330455318804566E-12$$

$$a_{10}=a_1·r^{n-1}=111\cdot {0.018018018018018018}^{10-1}=111\cdot {0.018018018018018018}^9=111\cdot 2.001534829771052E-16=2.2217036610458676E-14$$